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First occurrence of n in A306722.
2

%I #18 Apr 09 2019 04:13:37

%S 11,1,3,10,27,60,72,120,180,270,480,252,1155,720,792,1260,630,1050,

%T 4590,1680,1320,7980,3780,4680,5880,5040,5460,4620,9180,10080,10710,

%U 6930,9240,7560,21420,20790,27300,52080,15120,13860,48510,23940,62370,46200,16380,30030

%N First occurrence of n in A306722.

%C Record values: 11, 27, 60, 72, 120, 180, 270, 480, 1155, 1260, 4590, 7980, 9180, 10080, 10710, 21420, 27300, 52080, 62370, 191520, 207480, 214200, 428400, ..., .

%H Robert G. Wilson v, <a href="/A307245/b307245.txt">Table of n, a(n) for n = 0..876</a>

%e a(0) = 11 because (2*11)^2 = 484 is the smaller integer that can't be written as (p-1)*(q-1) with p,q primes, p < q.

%e a(3) = 10 because (2*10)^2 = 400 is the smaller integer such that the Diophantine equation (p-1)*(q-1) = 400 has three solutions: (p,q) = (2,401) = (5,101) = (11,41); also, phi(2*401) = phi(5*101) = phi(11*41) = 20^2.

%t f[n_] := Length@ Select[ Divisors[ 4n^2], # < 2n && PrimeQ[# +1] && PrimeQ[4n^2/# +1] &]; t[_] := 0; k = 1; While[k < 100000, a = f@k; If[t[a] == 0, t[a] = k]; k++]; t@# & /@ Range[0, 50]

%Y Cf. A039770, A247129, A306722.

%K nonn

%O 0,1

%A _Bernard Schott_ and _Robert G. Wilson v_, Mar 30 2019